A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space with the Discontinuous Galerkin (DG) method in time. As such, it combines the advantages of both the VE and the DG methods. The proposed scheme is implicit and it is proved to be unconditionally stable and accurate in space and time.

翻译：针对（线性）标量耗散波动方程，提出一种新型时空离散化方法。该方法基于结构化思路：将空间离散中的虚拟单元法（VE）与时间离散中的间断伽辽金法（DG）进行张量积实现。由此，该方法兼具虚拟单元法与间断伽辽金法的优势。所提格式为隐式格式，且被证明在空间和时间上具有无条件稳定性和精确性。